Icons vs. Symbols

The students completed their tip to Detroit (without me) and were still excited about the experience the day after when I returned to the classroom. They knew that they were supposed to create a “trip-line” to document their trip but before they could get started on it they had to understand that the “trip-line” is made up of icons, which brings up the question, what is an icon? The curriculum teaches this by explaining the difference between a symbol and an icon. The example given in the book was centered on the number thirteen. Three representations were shown – thirteen small stars, the Arabic Numeral 13, and the Roman Numeral XIII. The thirteen stars were considered an icon because thirteen stars were shown, the Arabic Numeral 13 was a symbol because it was man-made and we have agreed that the numerals 1 and 3 next to each other represent the quantity thirteen, and the Roman Numeral XIII was a mixes symbol because the X is a symbol and the three I’s can be seen as icons. At this point the students are completely lost and the next step is to have them create their own chart of symbols and icons. The teacher, a math Professor from Eastern Michigan University who helps in the class weekly, and I were trying to come up with another example that might hit a little closer to home and I thought of Nike shoes. The icon would be a basketball shoe and the symbol would be the swoosh (the check-mark that appears on everything Nike makes). I went up to the board to explain this new example for my first every impromptu teaching moment. The explanation went pretty well and the students were starting to distinguish between the two representations and by the end of the class each group in the class was able to share a different icon/symbol pair. This lesson about symbols and icons seemed so out of place to me during the class but after some reflection (and some help from others involved in the AP) I realized that the ability to represent an item with a symbol is a fundamental concept in algebra and in math in general. Had I (or the other teachers) made this connection during the class we could have offered a more complete and insightful explanation of the difference between icons and symbols and even encouraged the students to make their own symbols as mathematicians, scientists and engineers do when they create mathematical models.

My First Day

This academic year I am working in Mrs. Mill’s Algebra Project (AP) classroom at Ypsilanti High School. It is a freshman class comprised of 20 students who have committed to participate in the Algebra Project for all four years of their high school math education. The AP classroom model (originally created by Bob Moses) strives to prepare students for “full citizenship in today’s technological society” by emphasizing the understanding of the fundamental language of mathematics to ensure comprehension of mathematical concepts.

The algebra project begins with a trip, and my first day in the classroom was the day of the practice trip around the school before the actual trip to Detroit. Before we left to explore the school the students read a skit that provided directions and encouraged students to make predictions. The predictions focused around the normal questions – “Where are you going?” “What are you going to see?” and “What are you going to do?” All the students shared their predictions and I approached one student who had a very unique answer to the “what are you going to do?” question – it was a string of violent actions including punching, kicking, and slapping. I asked if he really thought that was going to happen on our trip and he responded, “I’m not going to but somebody probably will.” Sure enough, toward the end of the trip, one girl had gotten bored and tried to kick her leg in the air and touch her toe just as another student walked around the corner (it was a complete accident and both students started to laugh about it). The student’s prediction (at least part of it) came true.

In addition to taking the mini-trip, I introduced myself to the students, told them why I was there (to help them with math and show them cool things relating to engineering and technology), and told them about my research. I brought a poster of my research to help me explain my work to the students but at the last minute I decided to take a different approach that would get them more involved. I put the title of my project on the board – Active Knits: Smart Material Actuators. Instead of just telling them what I do I led them through a discussion of each of the words in the title to help them discover what Active Knits are on their own. They related Active to moving, Knits to clothing, Smart Material to a material that did something, and I helped them come to the conclusion that an Actuator is a motor. For this they understood that I made knits that moved. The students sit in groups of four students and I gave each group a different active knit. I walked around and heated each with a lighter so they could see the metal fabric contract, roll, arch, and twist. The students loved being able to hold and stretch the prototypes I gave them and they came up with insightful questions like what the applications are and if I could make it move by doing something different besides heating them.

My first day was great and I'm really looping forward to working with this small group of enthusiastic students.